A common method of metering gases involves passing the gas through a flow tube or orifice plate and measuring the pressure drop produced. Flow depends not only on the pressure drop, however, but also on the relative density of the gas. The latter must be measured independently in order to calibrate the meter and obtain accurate flow measurements for gases of varying composition. It is also often necessary to convert volumetric flow measurements of gases to mass flow or vice versa. Either of these conversions must use the relative density of the gas.
With gaseous fuels it is sometimes necessary to determine the Wobbe index, which is the heating value divided by the square root of the density. Gases of equal Wobbe index have similar burning characteristics and can be interchanged with each other before delivery of fuel to a customer. The Wobbe index can be calculated from measurements of heating value and relative density.
There are many other uses for the relative density in commerce in addition to these. The present invention is a novel method for measuring relative density that has important advantages over the state of the art.
Previous methods of measuring relative density can be divided into two categories. In the first category are those methods in which a known volume of the gas is actually weighed and compared to the weight of an equal volume of air. These methods have the disadvantage of requiring expensive equipment for precise weight measurement and also precisely controlling the pressure in this fixed volume. The pressure will determine the amount of gas that is weighed during each measurement; so it must be fixed.
The second category of methods are those in which a physical effect is used that depends on gas density. The magnitude of the effect in the unknown gas is compared to that in air. One method in this category measures the vibration frequency of a tuning fork or beam that is suspended in the gas.
A particularly simple physical effect that can be accurately measured is the flow of the gas through an orifice at a fixed pressure drop. In the orifices commonly used in flow measurement this flow depends not only on the density but also on a discharge coefficient that varies with Reynolds number. Well known graphs that give the discharge coefficient as a function of orifice design and Reynolds number are published in standard engineering texts and handbooks. With density changes of 2:1 it is possible under some conditions for the discharge coefficient to vary by 20% or more at the same flow. The orifices used for gas flow measurement are thus not satisfactory for accurately measuring relative density because of the complexities introduced by the presence of this additional variable in the relationship.
Gas flow measurements are usually carried out using orifice diameters that are 0.2 to 0.75 of the pipe diameter. Pressure drops across the orifice are measured in inches of water. Under these conditions, the flow is considered adiabatic through the orifice. There will, however, be temperature changes and other difficult-to-analyze effects and it is these which have been empirically collected together in the "discharge coefficient" for engineering design purposes.
I have discovered that by using a very small orifice or pore different flow conditions are established. Surprisingly, the varying discharge coefficient is no longer observed, and the elimination of this variable makes it possible to measure relative density as a simple (inverse square) function of flow rate.